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On p -adic L -functions of G L ( 2 ) × G L ( 2 ) over totally real fields

Haruzo Hida (1991)

Annales de l'institut Fourier

Let D ( s , f , g ) be the Rankin product L -function for two Hilbert cusp forms f and g . This L -function is in fact the standard L -function of an automorphic representation of the algebraic group G L ( 2 ) × G L ( 2 ) defined over a totally real field. Under the ordinarity assumption at a given prime p for f and g , we shall construct a p -adic analytic function of several variables which interpolates the algebraic part of D ( m , f , g ) for critical integers m , regarding all the ingredients m , f and g as variables.

On the infinite fern of Galois representations of unitary type

Gaëtan Chenevier (2011)

Annales scientifiques de l'École Normale Supérieure

Let E be a CM number field, p an odd prime totally split in  E , and let  X be the p -adic analytic space parameterizing the isomorphism classes of  3 -dimensional semisimple p -adic representations of  Gal ( E ¯ / E ) satisfying a selfduality condition “of type U ( 3 ) ”. We study an analogue of the infinite fern of Gouvêa-Mazur in this context and show that each irreducible component of the Zariski-closure of the modular points in  X has dimension at least 3 [ E : ] . As important steps, and in any rank, we prove that any first order...

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